UV Unwrapping Woes - Extra Faces?
First of all lets start by pointing out what's not ok with your mesh.




It seems that you have there not one coin but three of them. As pointed by @Matt you can select loose parts by hovering over them and pressing L. Remove both of them.
After deleting them Select All (A) then W > Remove Doubles.
If you want to select UV Island in UV Image Editor and see it in 3D view as well, you need to check Keep UV and Edit Mode selection in sync option (marked on the screenshot). Remember to be in Face Select mode if you want to use Island Selection (L).





Consider filling top and bottom faces with Triangle Fan or Grid Fill (based on mesh purpose) as ngons could not be the best choice for texturing.





At the end don't forget to Recalculate Normals > Ctrl+N.


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